Tailscale is pretty easy to update and it's one of the few things that I think I should always update as connecting all my things is a bit worrying.
On RHEL 7:
sudo yum update tailscale
On Windows, you can download the new tailscale exe and install that directly. It will overwrite the previous.
I was able to do the update on RHEL without losing my connection which was great. Windows resulted in my connections going down and coming back up. It's not a big deal but something to be mindful off.